We briefly outline the context and notation of [1]} that we will also use. For a chamber \(\mathfrak {C}\subset \Theta \)  the equivalence from (REF ) induces an isomorphism \(\varphi _\mathfrak {C}\colon K_0(\mathcal {M}_\mathfrak {C})\rightarrow K_G\big (\mathbb {A}^3\big )=\operatorname{Rep}(G)\) . Here \(K_0(\mathcal {M}_\mathfrak {C})\)  denotes the \(K\) -group of sheaves supported on the preimage of the \(G\) -orbit for the origin under the resolution \(\mathcal {M}_\mathfrak {C}\rightarrow \mathbb {A}^3/G\) . Walls in \(\Theta \)  are cut out by hyperplanes \(\big (\sum _i\alpha _i\cdot \theta (\chi _i)=0\big )\)  for some characters \(\chi _i\in \operatorname{Irr}(G)\)  and integers \(\alpha _i\in \mathbb {Z}\) , though in general not all \(\theta \)  on such a hyperplane will be non-generic. The inequalities in [1]} have three different forms, each coming from exceptional subvarieties. Firstly, each exceptional curve \(C\subset G\text{\textnormal {-Hilb}}\,\mathbb {A}^3\)  gives an inequality of the form
\(\theta \big (\varphi _{\mathfrak {C}_0}(\mathcal {O}_C)\big )>0.\) 
